diff --git a/frontend/strategy.html b/frontend/strategy.html
index 9210248..8e36b21 100644
--- a/frontend/strategy.html
+++ b/frontend/strategy.html
@@ -352,9 +352,14 @@
             }
           }
           const uniqBE = bes.filter((v,i)=> i===0 || Math.abs(v - bes[i-1]) > 1e-6);
-          // extremes within sample
+          // extremes — include the grid samples AND the exact kink points (strikes)
+          // plus the sample bounds, since piecewise payoffs peak/trough at strikes
           let maxY = -Infinity, minY = Infinity;
           for (const y of ys) { if (y > maxY) maxY = y; if (y < minY) minY = y; }
+          for (const k of new Set([...legs.map(l=>l.strike), lo0, hi0])) {
+            const y = plAt(legs, net, k, this.minDTE);
+            if (y > maxY) maxY = y; if (y < minY) minY = y;
+          }
           // unbounded detection from the far-right slope of the expiration curve
           // (downside is always bounded since the underlying can't go below 0)
           const slopeR = (ys[Nd] - ys[Nd-1]) / (xs[Nd] - xs[Nd-1]);
@@ -447,10 +452,15 @@
           const lo = Math.max(0.01, spot - half), hi = spot + half;
           const expAt = this.minDTE;
           const N = 161;
+          // x-grid = evenly spaced points + the exact strike kinks (so payoff
+          // vertices — butterfly peak, condor body, etc. — render sharply)
+          const xGrid = [];
+          for (let i = 0; i <= N; i++) xGrid.push(lo + (hi-lo)*i/N);
+          for (const k of strikes) if (k > lo && k < hi) xGrid.push(k);
+          xGrid.sort((a,b)=>a-b);
           const expData = [], tnData = [];
           let yMin = Infinity, yMax = -Infinity;
-          for (let i = 0; i <= N; i++) {
-            const x = lo + (hi-lo)*i/N;
+          for (const x of xGrid) {
             const ye = plAt(legs, net, x, expAt);
             const yt = plAt(legs, net, x, this.dteOffset);
             expData.push([x, +ye.toFixed(2)]);
@@ -467,7 +477,7 @@
 
           // breakevens for light vertical lines
           const bes = [];
-          for (let i = 1; i <= N; i++) {
+          for (let i = 1; i < expData.length; i++) {
             const y0 = expData[i-1][1], y1 = expData[i][1];
             if ((y0 < 0 && y1 > 0) || (y0 > 0 && y1 < 0)) {
               const x = expData[i-1][0] + (0 - y0) * (expData[i][0]-expData[i-1][0]) / (y1 - y0);